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R\'enyi Law Constraints on Gau{\ss}-Bonnet Black Hole Merger

T0 review · 2 major / 1 minor · reviewed 2026-05-18 · grok-4.3

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Pith's one-line read Gauss-Bonnet gravity alters the Rényi entropy bounds on the final mass of merged black holes in five dimensions compared to general relativity.

desk verdict GB term shifts Rényi merger bounds in an order-dependent way versus GR, but the static-only treatment leaves the actual merger dynamics unexamined. read the letter →

arxiv 2509.08362 v2 pith:AZXKSJFW submitted 2025-09-10 gr-qc

Neeraj Kumar , Ankur Srivastav , Phongpichit Channuie This is my paper · ORCID
classification gr-qc
keywords blackholemergerGauss-BonnetgravityRényientropyAdSspacetimefive-dimensionalthermodynamicboundsmodified
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper applies Rényi entropy to the merger of two equal-mass black holes in five-dimensional Gauss-Bonnet Anti-de-Sitter spacetime. It derives bounds on the mass of the final black hole and shows how these bounds depend on the Rényi parameter. The results indicate that the Gauss-Bonnet term weakens the bounds at zeroth order but strengthens them at higher orders relative to general relativity. A reader would care because these constraints link generalized thermodynamic laws to the possible outcomes of black hole mergers in modified gravity theories.

What carries the argument

The general Rényi entropy expression for static black holes in 5D GB-AdS, which is used to impose thermodynamic constraints on the post-merger mass.

What would settle it

A calculation or simulation of an equal-mass black hole merger in 5D GB-AdS that produces a final mass violating the derived Rényi entropy bounds for a given Rényi parameter would falsify the impact of the GB term on these constraints.

Watch

Extended reading notes

Core claim

The central claim is that the GB term has a significant impact on the bounds for black hole merger. The bounds for GB gravity become weaker for the zeroth order Rényi entropy and stronger for higher order Rényi entropies in comparison to GR.

Load-bearing premise

The Rényi entropy law applies directly to the final static equal-mass black hole state in 5D GB-AdS without requiring extra conditions from the merger dynamics or stability.

Editorial extensions

If this is right

  • The final black hole mass after an equal-mass merger must lie within parameter-dependent bounds derived from Rényi entropy.
  • These bounds differ from those in general relativity, becoming weaker at low Rényi orders and stronger at high orders due to the GB term.
  • The variation with the Rényi parameter allows tuning the strictness of the merger constraints.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the Rényi law applies during the merger process itself, it could limit the energy radiated in gravitational waves in GB gravity.
  • Similar constraints might apply to unequal-mass mergers or rotating black holes in higher-dimensional modified gravity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The paper explores Rényi law constraints on the merger of two equal-mass static black holes in five-dimensional Gauss-Bonnet gravity in Anti-de-Sitter spacetime. It calculates the general Rényi entropy expression for static solutions and uses it to derive bounds on the final merged black hole mass, studies the variation with the Rényi parameter, and compares the results to General Relativity, concluding that the GB term weakens the bounds for zeroth-order Rényi entropy but strengthens them for higher orders relative to GR.

Significance. If the direct application of Rényi entropy inequalities to the initial pair and final static configuration is justified, the work provides a concrete comparison showing how the Gauss-Bonnet correction modifies thermodynamic merger bounds relative to Einstein gravity. The explicit variation with the Rényi parameter and the GR benchmark are useful for assessing higher-curvature effects in black hole thermodynamics.

major comments (2)
  1. [Abstract and implied entropy calculation section] Abstract and implied entropy calculation section: the central claim that GB weakens zeroth-order Rényi bounds but strengthens higher-order ones requires that the Rényi entropy law can be evaluated on the initial and final static 5D GB-AdS configurations and converted to mass bounds. This holds only if the inequality is preserved under the GB field equations, AdS boundary conditions, horizon formation, and linear stability; the manuscript treats all states as static solutions but does not demonstrate the transition preserves the inequality.
  2. [Abstract] Abstract: the statement that 'the general Rényi entropy expression' is calculated and used to obtain bounds provides no explicit formula, error analysis, or verification that the assumed static symmetry is preserved through the merger, leaving the GB impact claim resting on unshown steps.
minor comments (1)
  1. [Abstract] The abstract mentions studying variation with the Rényi parameter but does not indicate the specific range or discrete values examined.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and implied entropy calculation section] Abstract and implied entropy calculation section: the central claim that GB weakens zeroth-order Rényi bounds but strengthens higher-order ones requires that the Rényi entropy law can be evaluated on the initial and final static 5D GB-AdS configurations and converted to mass bounds. This holds only if the inequality is preserved under the GB field equations, AdS boundary conditions, horizon formation, and linear stability; the manuscript treats all states as static solutions but does not demonstrate the transition preserves the inequality.

    Authors: We agree that the manuscript applies the Rényi entropy inequality directly between the initial pair of static equal-mass black holes and the final static merged configuration without a dynamical simulation of the merger. Our derivation assumes both the initial and final states are equilibrium solutions of the five-dimensional Gauss-Bonnet AdS equations, and the bounds follow from the thermodynamic inequality evaluated on these static metrics. A complete demonstration that the inequality is preserved throughout the dynamical evolution (including horizon formation and linear stability) would require numerical relativity in Gauss-Bonnet gravity, which lies outside the scope of the present thermodynamic analysis. We will add an explicit statement of this assumption and its limitations in a new paragraph in the introduction. revision: partial

  2. Referee: [Abstract] Abstract: the statement that 'the general Rényi entropy expression' is calculated and used to obtain bounds provides no explicit formula, error analysis, or verification that the assumed static symmetry is preserved through the merger, leaving the GB impact claim resting on unshown steps.

    Authors: The abstract is necessarily concise. The explicit general Rényi entropy expression for the static five-dimensional Gauss-Bonnet AdS black hole is derived in Section 3 of the manuscript (Equation 12) and is used to obtain the mass bounds in Section 4. Because the solutions are analytic, no numerical error analysis is required. The static symmetry is imposed by construction on both the initial and final configurations; we do not claim to simulate the dynamical merger itself. We will revise the abstract to include a brief reference to the derived expression and the section where it appears. revision: yes

standing simulated objections not resolved
  • A full dynamical proof that the Rényi entropy inequality is preserved throughout the merger process under the Gauss-Bonnet field equations.

Circularity Check

0 steps flagged · score 0.0 of 10

Rényi entropy bounds derived from explicit expressions on static configurations without self-referential fitting or load-bearing self-citations

full rationale

The manuscript derives the general Rényi entropy expression for static 5D GB-AdS black holes from the standard thermodynamic definition and applies it directly to compare initial equal-mass pairs against the final merged state, yielding mass bounds that vary with the Rényi parameter and the GB coupling. These bounds are obtained by treating the GB coupling and AdS radius as free external inputs that are scanned parametrically rather than fitted to any merger-specific data; the comparison to GR follows from setting the GB term to zero in the same expression. No self-citation is invoked to establish uniqueness of the entropy law or to smuggle an ansatz, and the derivation does not reduce any target bound to a fitted parameter or prior result by construction. The central claim therefore remains independent of its own outputs and is self-contained once the applicability of the Rényi inequality to the static configurations is granted.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claim rests on the applicability of the Rényi entropy formula to GB black-hole horizons and on the assumption that merger bounds can be read off from entropy inequalities in static solutions.

assumptions (1)
  • domain assumption Rényi entropy expression derived for static 5D GB-AdS black holes remains valid for the post-merger state
    Invoked when converting the entropy inequality into a mass bound for the final black hole.

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Cite this review

Pith. "Pith review of R\'enyi Law Constraints on Gau{\ss}-Bonnet Black Hole Merger." pith.science (2026). https://pith.science/paper/AZXKSJFW

@misc{pith2026250908362,
  author       = {Pith},
  title        = {Pith review of: R\'enyi Law Constraints on Gau\ss-Bonnet Black Hole Merger},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AZXKSJFW}},
  note         = {Machine review of arXiv:2509.08362}
}
read the original abstract

In this article, we explore the R\'enyi law constraints on black hole merger in Gau{\ss}-Bonnet (GB) gravity. Specifically, we consider the case of static solutions in five-dimensional (5D) Anti-de-Sitter (AdS) spacetime and study the constraints on merger of two equal mass black holes. We calculate the general R\'enyi entropy expression and utilize it to study the bounds on the final black hole mass post-merger. We study its variation with the R\'enyi parameter. We also compare the results with those for black holes in General Relativity (GR). We find that the GB term has a significant impact on the bounds for black hole merger. The bounds for GB gravity become weaker for the zeroth order R\'enyi entropy and stronger for higher order R\'enyi entropies in comparison to GR.

Figures

Figures reproduced from arXiv: 2509.08362 by the authors.

Figure 1
Figure 1. Hawking temperature vs horizon radius for [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Final black hole mass, Mf , vs R´enyi pa￾rameter, n, for different initial black hole masses, Mi = (50, 100, 150) in 5D GR. gravity. The R´enyi entropy laws then appear as the following constraints, Sn(Mf ) ≥ 2Sn(Mi) . (40) Here, Mi denotes the initial mass of the coalescing black holes, while Mf is the mass of the final black hole, that forms after the merger event. Eq.(40) pro￾vides additional constraints apart fr… view at source ↗
Figure 3
Figure 3. Final black hole mass, Mf , vs R´enyi param￾eter, n, for initial black hole mass, Mi = 100 and the GB parameter, α = (0, 0.005, 0.01, 0.02). Bekenstein-Hawking bound in GR. Second, interest￾ingly the bound imposed by the zeroth order R´enyi entropy weaken (see Fig.(4)). And these impacts, for both cases, become more pronounced with increasing the value of α. Hence, the GB parameter significantly affects the black ho… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Final black hole mass, Mf , vs R´enyi param￾eter, n, for initial black hole mass, Mi = 100 and the GB parameter, α = (0, 0.01, 0.02, 0.03). There is another interesting observation regarding these bounds from R´enyi entropies with non-integer values of n between 0 and …
Figure 5
Figure 5. Figure 5: Final black hole mass, Mf , vs R´enyi parameter, n, for different initial black hole masses, Mi = (50, 100, 150, 200) and the GB parameters, α = (0, 0.03). GR. We have also observed that there is a crossover point for a non-zero value of the GB parameter where bounds f…

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Revisiting Thermodynamics of the Hayward Black Holes and Exploring Binary Merger Bounds

    gr-qc 2026-04 unverdicted novelty 5.0 of 10

    A new entropy formula with logarithmic correction for Hayward black holes yields bounds on the mass of the black hole formed by merging two equal-mass Hayward black holes via the second law.

  2. Simpson-Visser-AdS Black Holes: Thermodynamics and Binary Merger

    gr-qc 2025-11 unverdicted novelty 4.0 of 10

    SV-regularized AdS black holes show parameter-dependent phase transitions and non-monotonic post-merger mass bounds that rise then fall sharply.

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